Answer:
The length of the longest side of the triangle is 13 inches
Step-by-step explanation:
step 1
Find the value of x
we know that
The perimeter of triangle is equal to the sum of its three length sides
so
[tex]P=x+(2x+3)+(4x-8)[/tex]
[tex]P=(7x-5) \ in[/tex]
we have
[tex]P=30\ in[/tex]
substitute
[tex]30=(7x-5)[/tex]
solve for x
[tex]7x=30+5\\7x=35\\x=5[/tex]
step 2
Find the length of the longest side of the triangle
Remember that in a right triangle, the longest side is the hypotenuse
so
(2x+3) is the longest side
substitute the value of x
[tex]2(5)+3=13\ in[/tex]
